To add fractions with the same or like denominator, we simply add the numerators and then copy the common denominator. Always reduce your answer to the lowest terms.

Here, the numerators are \(a\) and \(b\), and the common denominator is \(d\).

$${a \over d} + {b \over d} = {{a + b} \over d}$$

Example 1: \(\large{{2 \over 7} + {3 \over 7}}\)

Add the numerators \(2\) and \(3\), we get \( 2 + 3 = 5\). Next, we copy the common or like denominator which is \(7\).

$$\eqalign{

{2 \over 7} + {3 \over 7} &= {{2 + 3} \over 7} \cr

&= {5 \over 7} \cr} $$

This is already in the lowest terms since the numerator and denominator have no common denominator other than \(1\).

Example 2: \(\large{{5 \over {14}} + {3 \over {14}}}\)

They have the same denominator so this is an easy problem. We add the numerators \(5\) and \(3\) to get \(8\). Then, we copy the common or like denominator which is \(14\). Finally, simplify by dividing the numerator and denominator by the GCF which is \(2\).

$$\eqalign{

{5 \over {14}} + {3 \over {14}} &= {{5 + 3} \over {14}} \cr

& = {8 \over {14}} \cr

& = {{8 \div 2} \over {14 \div 2}} \cr

& = {4 \over 7} \cr} $$